Adsorption experiments were done at four different pressures 1. C with zeolite 13X as the adsorbent. To explain the equilibrium adsorption capacity, the Langmuir-Freundlich isotherm model was adopted, and the parameters of the isotherm equation were fitted to the experimental data for a wide range of pressures and temperatures.
Then, dynamic simulations were performed using the system equations for material and energy balance with the equilibrium adsorption isotherm data. The optimal mass transfer and heat transfer coefficients were determined after iterative calculations. As a result, the dynamic variable mass transfer model can estimate the adsorption rate for a wide range of concentrations and precisely simulate the fixed-bed adsorption process of a flue gas mixture of carbon dioxide and nitrogen. Numerical analysis of mass transfer with graphite oxidation in a laminar flow of multi-component gas mixture through a circular tube.
In the present paper, mass transfer has been numerically studied in a laminar flow through a circular graphite tube to evaluate graphite corrosion rate and generation rate of carbon monoxide during a pipe rupture accident in a high temperature gas cooled reactor. Multi-component diffusion coefficients were used in a diffusion term. Mass conservation equations of each gas component, mass conservation equation and momentum conservation equations of the gas mixture were solved by using SIMPLE algorism.
Chemical reactions between graphite and oxygen, graphite and carbon dioxide, and carbon monoxide combustion were taken into account in the present numerical analysis. An energy equation for the gas mixture was not solved and temperature was held to be constant in order to understand basic mass transfer characteristics without heat transfer. But, an energy conservation equation for single component gas was added to know heat transfer characteristics without mass transfer.
The effects of these chemical reactions on the mass transfer coefficients were quantitatively and qualitatively clarified in the range of 50 to of inlet Reynolds numbers, 0 to 0. As stricter environmental regulation have led to an increase in the water treatment cost, it is necessary to quantitatively study the input power of the aeration process to improve the energy efficiency of the water treatment processes.
The objective of this study is to propose the empirical correlations for the mass transfer coefficient with the gas hold-up and input power in order to investigate the mass transfer characteristics of the aeration process. It was found that as the input power increases, the mass transfer coefficient increases because of the decrease of gas hold-up and increase of Reynolds number, the penetration length, and dispersion of mixed flow.
Characterisation of the volatile profiles of infant formulas by proton transfer reaction- mass spectrometry and gas chromatography- mass spectrometry. Directory of Open Access Journals Sweden. Full Text Available In this study, the effect of pH on the mass transfer of oxygen bubble swarms in non-Newtonian fluids was experimentally studied. The volumetric liquid side mass transfer coefficient kLa, liquid side mass transfer coefficient kL, and specific interfacial area a were investigated.
It was found that the kLa increased with the gas flow rate increasing and decreased with the apparent viscosity of the liquid increasing. In the case of pH 7 was attributed to the decomposition of the Xanthan molecular structure by the hydroxyl of NaOH. In this study, the Euler-Euler and Euler-Lagrange modeling approaches were applied to simulate the multiphase flow in the water model and gas -stirred ladle systems.
Detailed comparisons of the computational and experimental results were performed to establish which approach is more accurate for predicting the gas -liquid multiphase flow phenomena. It was demonstrated that the Euler-Lagrange approach is more accurate than the Euler-Euler approach.
The Euler-Lagrange approach was applied to study the effects of the free surface setup, injected bubble size, gas flow rate, and slag layer thickness on the slag-steel interaction and mass transfer behavior. Significant inaccuracies in the prediction of the surface fluid flow characteristics were found when the flat free surface was assumed. The variations in the main controlling parameters bubble size, gas flow rate, and slag layer thickness and their potential impact on the multiphase fluid flow and mass transfer characteristics turbulent intensity, mass transfer rate, slag-steel interfacial area, flow patterns, etc.
It was revealed that by injecting finer bubbles as well as by properly increasing the gas flow rate and the slag layer thickness, the ladle refining efficiency can be enhanced significantly. During high-temperature confocal scanning laser microscopy HT-CSLM of liquid steel samples, thermal Marangoni flow and rapid mass transfer between the sample and its surroundings occur due to the relatively small sample size diameter around 5 mm and large temperature gradients.
The resulting evaporation and steel-slag reactions tend to change the chemical composition in the metal. Such mass transfer effects can change observed nonmetallic inclusions. This work quantifies oxide-metal- gas mass transfer of solutes during HT-CSLM experiments using computational simulations and experimental data for 1 dissolution of MgO inclusions in the presence and absence of slag and 2 Ca, Mg-silicate inclusion changes upon exposure of a Si-Mn-killed steel to an oxidizing gas atmosphere.
Two-phase heat and mass transfer in turbulent parallel and countercurrent flows of liquid film and gas. Kholpanov, L. Obshchej i Neorganicheskoj Khimii. To determine the ways of intensification of heat and mass transfer processes, the direct flow and counterflow heat and mass transfer is analytically investigated during the turbulent flow of a liquid and gas film on the basis of solving the energy equation for liquid and gas film, i.
The analysis of the two-phase heat transfer has shown that it is necessary to know the position of each point in a plane before using this or that formula. Depending on its position on this plane, the heat transfer process will be determined by one or two phases only.
It is found, that in the case of a single-phase heat transfer the temperature on the surface remains stable over the channel length. In the case of a two-phase heat transfer it can significantly change over the channel length [ru. The influence of polymeric membrane gas spargers on hydrodynamics and mass transfer in bubble column bioreactors. Gas sparging performances of a flat sheet and tubular polymeric membranes were investigated in 3.
Air-water and air-CMC Carboxymethyl cellulose solutions of 0. CMC solutions were employed in the study to simulate rheological properties of bioreactor broth. Gas holdup, bubble size distribution, interfacial area and gas -liquid mass transfer were studied in the homogeneous bubbly flow hydrodynamic regime with superficial gas velocity U G range of 0.
The study indicated that the tubular membrane sparger produced the highest gas holdup and densely populated fine bubbles with narrow size distribution.
An increase in liquid viscosity promoted a shift in bubble size distribution to large stable bubbles and smaller specific interfacial area. The tubular membrane sparger achieved greater interfacial area and an enhanced overall mass transfer coefficient K L a by a factor of 1. Liquid- gas mass transfer at drop structures. In this study, experimental work was carried out to analyze the influence of characteristics of drops on reaeration.
Physical models were built, mimicking typical In total, tests were performed. Based on their results, empirical expressions translating the relationship between the mass transfer of oxygen and physical parameters of drop structures were Then, by applying the two-film theory with two-reference substances, the relation to hydrogen sulfide release was defined.
By quantifying the air-water mass transfer rates Gas -liquid mass transfer in a cross-flow hollow fiber module : Analytical model and experimental validation. The cross-flow operation of hollow fiber membrane contactors offers many advantages and is preferred over the parallel-flow contactors for gas -liquid mass transfer operations. However, the analysis of such a cross-flow membrane gas -liquid contactor is complicated due to the change in concentrations.
Handbook of heat and mass transfer. Volume 2. This two-volume series, the work of more than contributors, presents advanced topics in industrial heat and mass transfer operations and reactor design technology. Volume 2 emphasizes mass transfer and reactor design. Mass transfer principles with homogeneous and heterogeneous reactions. Convective diffusion with reactions in a tube.
Transient mass transfer onto small particles and drops. Modeling heat and mass transport in falling liquid films. Heat and mass transfer in film absorption. Multicomponent mass transfer : theory and applications. Diffusion limitation for reaction in porous catalysts. Kinetics and mechanisms of catalytic deactivation.
Mixture boiling. Estimating vapor pressure from normal boiling points of hydrocarbons. Estimating liquid and vapor molar fractions in distillation columns. Principles of multicomponent distillation. Generalized design methods for multicomponent distillation. Interfacial films in inorganic substances extraction. Liquid-liquid extraction in suspended slugs. Mass transfer and kinetics in three-phase reactors. Estimating liquid film mass transfer coefficients in randomly packed columns. Designing packed tower wet scrubbers - emphasis on nitrogen oxides.
Gas absorption in aerated mixers. Axial dispersion and heat transfer in gas -liquid bubble columns. Operation and design of trickle-bed reactors. Specialists' meeting on heat and mass transfer in the reactor cover gas , Harwell, England, October The meeting was presided over by Dr K.
Eickhoff of the United Kingdom. The following topical areas were reviewed and discussed during the meeting: 1. National review presentations on the status of activities on heat and mass transfer in the reactor cover gas - 2 papers; 2.
Aerosol dynamics - 4 papers; 3. Aerosol trapping - 2 papers; 4. Heat and mass transfer through cover gas in annuli - 3 papers; 5.
Radiative properties - 4 papers; 6. Modelling of cover gas - 4 papers. A separate abstract was prepared for each of these papers.
On the basis of papers presented and discussed by participants, session summaries and conclusions were drafted on the above topical areas. These summaries, as well as general conclusions and recommendations of the meeting were reviewed and agreed upon by consensus at the end of the meeting. This study proposed a submerged hollow fibre membrane bioreactor HFMBR system capable of achieving high carbon monoxide CO mass transfer for applications in microbial synthesis gas conversion systems.
Hydrophobic polyvinylidene fluoride PVDF membrane fibres were used to fabricate a membrane module, which was used for pressurising CO in water phase. A higher k L a of All rights reserved. Experimental and analytical studies of iodine mass transfer from xenon-iodine mixed gas bubble to liquid sodium pool. In the fuel pin failure accident of a liquid metal fast reactor, volatile fission products play an important role in the assessment of radiological consequences.
Especially the radioisotopes of elemental iodine are important because of their high volatility and of the low permissible dose to human thyroid.
The released iodines are known to be retained in the coolant sodium as sodium iodide due to the chemical affinity between alkali metals and halogens. However, the xenon and krypton released with iodines into the sodium pool as bubbles may influence the reaction rate of iodine with sodium during the bubble rising.
So far, the only few experimental results have been available concerning the decontamination factor DF: the ratio of the initial iodine mass in the mixed gas bubble to the released mass into the cover gas of iodine in this phenomenon.
Therefore, experimental and analytical studies were carried out to study the mass transfer of iodine from a xenon-iodine mixed gas bubble to the liquid sodium pool. In the experiments, the bubble was generated in the sodium pool by cracking a quartz ball which contains the xenon-iodine mixed gas and then, the mixed gas released into the argon cover gas was collected to determine the transferred iodine mass into the pool.
A rising velocity of the bubble was measured by Chen-type void sensors arranged vertically in the pool. From the measured rising velocity and another observation of bubble behavior in simulated water experiments, it is found that the generated bubble breaks up into several smaller bubbles of spherical cap type during the rising period. Transferred iodine mass per unit initial bubble volume from the bubble to the sodium pool shows increases with increasing time and the initial iodine concentration.
A mass transfer rate obtained by differentiating the transferred iodine mass with respect to the time indicates a rapid decrease just after the bubble generation and a slow decrease for the successive period. Mass transfer with complex chemical reactions in gas -liquid systems: two-step reversible reactions with unit stoichiometric and kinetic orders. This model has been used to determine mass transfer rates, enhancement factors and concentration profiles over a wide range of process conditions.
Theoretical studies on membrane-based gas separation using computational fluid dynamics CFD of mass transfer. A 2D mass transfer model was developed to study carbon dioxide removal by absorption in membrane contactors. The model predicts the steady state absorbent and carbon dioxide concentrations in the membrane by solving the conservation equations. The continuity equations for three sub domains of the membrane contactor involving the tube; membrane and shell were obtained and solved by finite element method FEM.
The model was based on 'non-wetted mode' in which the gas phase filled the membrane pores. Laminar parabolic velocity profile was used for the liquid flow in the tube side; whereas, the gas flow in the shell side was characterized by Happel's free surface model.
Axial and radial diffusion transport inside the shell, through the membrane, and within the tube side of the contactor was considered in the mass transfer model. The modeling predictions were in good agreement with the experimental values for different values of gas and liquid flow rates. Determination of volumetric gas -liquid mass transfer coefficient of carbon monoxide in a batch cultivation system using kinetic simulations.
A mathematical model of microbial kinetics was introduced to predict the overall volumetric gas -liquid mass transfer coefficient k L a of carbon monoxide CO in a batch cultivation system. The cell concentration X , acetate concentration C ace , headspace gas N co and [Formula: see text] , dissolved CO concentration in the fermentation medium C co , and mass transfer rate R were simulated using a variety of k L a values.
The C co values decreased with increase in cultivation times, whereas the maximum mass transfer rate was achieved at the mid-log phase due to vigorous microbial CO consumption rate higher than R.
The model suggested in this study may be applied to a variety of microbial systems involving gaseous substrates. Mass transfer apparatus and method for separation of gases. A process and apparatus for separating components of a source gas is provided in which more soluble components of the source gas are dissolved in an aqueous solvent at high pressure.
The system can utilize hydrostatic pressure to increase solubility of the components of the source gas. The apparatus includes gas recycle throughout multiple mass transfer stages to improve mass transfer of the targeted components from the liquid to gas phase. Separated components can be recovered for use in a value added application or can be processed for long-term storage, for instance in an underwater reservoir.
Mass transfer in counter current flows. Doichinova, Maria D. A theoretical analysis of gas -liquid counter-current flow in laminar boundary layers with flat phase boundary based on similarity variables method has been done.
The obtained numerical results for the energy dissipation, mass transfer rate and their ratio are compared with analogous results for concurrent flows. A diffusion type of model is proposed for modeling of the mass transfer with chemical reaction in the column apparatuses in the cases of circulation zones. The presence of rising and descending flows the change of the velocity direction leads to using three coordinate systems.
An iterative algorithm for the concentration distribution calculation is proposed. The influence of the zones breadths on the mass transfer efficiency in the column is investigated. Key words: efficiency, mass transfer , velocity distribution, column apparatuses, circulation zones. Experimental investigation of the liquid volumetric mass transfer coefficient for upward gas -liquid two-phase flow in rectangular microchannels.
Full Text Available The gas -liquid two-phase mass transfer process in microchannels is complicated due to the special dynamical characteristics. In this work, a novel method was explored to measure the liquid side volumetric mass transfer coefficient kLa.
Pressure transducers were utilized to measure the pressure variation of upward gas -liquid two-phase flow in three vertical rectangular microchannels and the liquid side volumetric mass transfer coefficient kLa was calculated through the Pressure-Volume-Temperature correlation of the gas phase. Carbon dioxide-water, carbon dioxide-ethanol and carbon dioxide-n-propanol were used as working fluids, respectively.
Results showed that the channel diameter and the capillary number influence kLa remarkably and that the maximum value of kLa occurs in the annular flow regime. A new correlation of kLa was proposed based on the Sherwood number, Schmidt number and the capillary number.
The predicted values of kLa agreed well with the experimental data. Numerical simulation study of gas -liquid reactive mass transfer along corrugated sheets with interface tracking.
This work is done within the framework of gas treatment and CO 2 capture process development. The main objective of the present work is to fill the gap between classical experiments and industrial conditions by the use of Computational Fluid Dynamics CFD. The physical problem considered corresponds to the liquid film flow down a corrugate surface under gravity in present of a gas phase.
The chemical species in the gas phase absorb in the liquid phase and react. Numerical calculations are carried out in order to determine the impact of physical and geometrical properties on reactive mass transfer in industrial operating conditions. Dimensionless groups for multidimensional heat and mass transfer in adsorbed natural gas storage.
Sphaier, L. Programa de Pos-Graduacao em Engenharia Mecanica. This paper provides a new methodology for analyzing heat and mass transfer in gas storage via adsorption. The foundation behind the proposed methodology comprises a set of physically meaningful dimensionless groups. A discussion regarding the development of such groups is herein presented, providing a fully normalized multidimensional formulation for describing the transport mechanisms involved in adsorbed gas storage.
After such presentation, data from previous literature studies associated with the problem of adsorbed natural gas storage are employed for determining realistic values for the developed parameters. Then, a one-dimensional test-case problem is selected for illustrating the application of the dimensionless formulation for simulating the operation of adsorbed gas reservoirs.
The test problem is focused on analyzing an adsorbed gas discharge operation. This problem is numerically solved, and the solution is verified against previously published literature data. The presented results demonstrate how a higher heat of sorption values lead to reduced discharge capacities. Effect of interaction between inclusions in a gas -liquid mixture on interphase heat and mass transfer. The effect of interaction between inclusions in a gas -liquid mixture on interphase heat and mass transfer is analyzed.
It is taken into account that inclusions bubbles or drops are not in a pure carrier phase, but in a disperse medium, mean properties of which are determined by the presence of other inclusions in it and by a temperature field around them. The consideration is carried out in the framework of two model of monodisperse mixture, i. The correlation functions method is shown to be effective for the both models.
Mean temperature fields around inclusions are determined along with the intensity of interphase heat and mass transfer. The dependences obtained are in a satisfactory agreement with experimental data. The dependence of interphase heat and mass transfer on the structure of disperse mixture is analyzed. Mixing and mass transfer in a pilot scale U-loop bioreactor. A system capable of handling a large volumetric gas fraction while providing a high gas to liquid mass transfer is a necessity if the metanotrophic bacterium Methylococcus capsulatus is to be used in single cell protein SCP production.
In this study mixing time and mass transfer coefficients we Influence of fluid-mechanical characteristics of the system on the volumetric mass transfer coefficient and gas dispersion in three-phase system. Full Text Available Distribution of gas bubbles and volumetric mass transfer coefficient, Kla, in a three phase system, with different types of solid particles at different operation conditions were studied in this paper. The experiments were carried out in a 2D plexiglas column, x 20,4 x mm and in a cylindrical plexiglas column, with a diameter of 64 mm and a hight of mm.
The Kla coefficient increased with gas and liquid velocities. Results showed that the volumetric mass transfer coefficient has a higher values in three phase system, with solid particles, compared with two phase system. The particles properties diameter and density have a major impact on oxygen mass transfer in three phase systems.
Gas hold-up and oxygen mass transfer in three pneumatic bioreactors operating with sugarcane bagasse suspensions. Sugarcane bagasse is a low-cost and abundant by-product generated by the bioethanol industry, and is a potential substrate for cellulolytic enzyme production.
Using large particles of untreated sugarcane bagasse, the loop-type bioreactors CTA and SCA exhibited higher mass transfer , compared to the BC reactor. These results demonstrated that pneumatic bioreactors can provide elevated oxygen transfer in the presence of vegetal biomass, making them an excellent option for use in three-phase systems for cellulolytic enzyme production by filamentous fungi.
Study of molecular iodine-epoxy paint mass transfer. Belval-Haltier, E [Inst. Paul-lez-Durance France. So, the objective of the present work was to evaluate which phase limited the adsorption process of iodine onto gaseous epoxy paint under a range of conditions which may be relevant to a severe reactor accident.
For each test condition, the initial deposition velocity was determined and the corresponding gas phase mass transfer , kg, was estimated by using the heat transfer analogy for a laminar flow passing over a flat plate.
Then, the surface reaction rate, Kr, was deduced from these two values. Experiments performed indicated that iodine adsorption onto epoxy paint is highly dependent on temperature, relative humidity of the carrier gas and moisture content of the painted coupon. In dry air flow conditions, the adsorption of iodine onto paint was found to increase with temperature and to be limited by the surface reaction rate, Kr. The same phenomenon has been observed with an increase of the initial water content of the painted coupon.
Flooding and mass transfer in Goodloe-packed columns, Part 2. Krypton gas is recovered from HTGR off- gas streams by countercurrent absorption in liquid carbon dioxide. Goodloe stainless steel wire mesh packing was chosen for the absorption columns since the process operates at 0 C and about 20 atm pressure.
Flooding points and an overall mass transfer coefficient for Goodloe-packed columns were determined with a carbon dioxide-air-water system for 6. Flood points were obtained for liquid-to- gas mass velocity ratios of 20 to Results indicated that this antifoam agent AFA increased gas holdup in the waste simulant by about a factor of four and, counter intuitively, that the holdup increased as the simulant shear strength decreased apparent viscosity decreased.
And whether the WTP air supply system being designed would have the capacity to handle a demand for increased airflow to operate the sparger-PJM mixing systems should the AFA increase retention of the radiochemically generated flammable gases in the waste by making the gas bubbles smaller and less mobile, or decrease the size of sparger bubbles making them mix less effectively for a given airflow rate.
Other elements of the new program include evaluating effects other variables could have on gas holdup in systems with AFA additions such as catalysis from trace noble metals in the waste, determining mass transfer coefficients for the AZ waste simulant, and determining whether other AFA compositions such as Dow Corning US could also increase gas holdup in Hanford waste.
This new testing program was split into two investigations, prototypic sparger. Heat-and- mass transfer during a laminar dissociating gas flow in eccentric annular channels. An algorithm to calculate heat-and- mass transfer processes during dissociating gas laminar flow in an eccentric annular channels is considered. Analytical solutions of the heat transfer equations for a rod clodding and gap with boundary conditions of conjugation of temperatures and heat fluxes have been used to determine temperature field.
This has made it possible to proceed from slution of the conjugate problem to solution of the equation of energy only for the coolant. The results of calculation of temperature distribution along the cladding for different values of its eccentricity and thermal conductivity coefficient both for the case of frozen flow and in the presence of chemical reactions in the flow are given.
When calculating temperatures with conjugation boundary conditions temperature gradients in azimuthal direction are far less and heat transfer in concentration diffusion is carried out mainly in radial direction.
To the generalization of experimental data on heat and mass transfer in evaporation and condensation. Similarity equations for heat-and- mass transfer in binary gas or steam- gas layers in the processes of liquid evaporation, condensation and desublimation of vapours, desorption and absorption and porous body cooling are considered.
It is accepted that steam- gas components obey to the equation of ideal gas state and that evaporation and condensation condititons permit to neglect the influence of compressability of gas steam- gas mixture, non-isothermality of boundary layer and interphase kinetic resistance to mass transfer onto the interfaces.
It is concluded that the results of considered experimental and theoretical investigations of the above processes are in a satisfactory agreement and show insignificance of the effect of hydrodynamic conditions determining the regime of main steam- gas mixture flow on relative heat-and- mass transfer coefficients.
According to the theoretical calculation results with increase of the factor of M steam- gas mixture non-uniformity mass transfer intensity in evaporation decreases, while in condensation it grows, but M effect on the mass transfer coefficient is rather small and sowhat increases in the case of a turbulent boundary layer evaporation. In condensation it is less than in evaporation. Ozone mass transfer behaviors on physical and chemical absorption for hollow fiber membrane contactors.
To understand the mass transfer behaviors in hollow fiber membrane contactors, ozone fluxes affected by various conditions and membranes were investigated. For physical absorption, mass transfer rate increased with liquid velocity and the ozone concentration in the gas.
Gas flow rate was little affected when the velocity was larger than the critical value, which was 6. For chemical absorption, the flux was determined by the reaction rate between ozone and the absorbent.
Therefore, concentration, species, and pH affected the mass transfer process markedly. For different absorbents, the order of mass transfer rate was the same as the reaction rate constant, which was phenol, sodium nitrite, hydrogen peroxide, and oxalate.
The results showed the process was controlled by liquid film and the gas phase conditions, and membrane properties did not affect the ozone flux. For the chemical absorption, gas film, membrane and liquid film affected the mass transfer together, and none of them were negligible.
The effect of diffusivity on gas -liquid mass transfer in stirred vessels. Experiments at atmospheric and elevated pressures. Mass transfer has been studied in gas -liquid stirred vessels with horizontal interfaces which appeared to the eye to be completely smooth. Special attention has been paid to the influence of the coefficient of molecular diffusion. The results are compared with those published before. The simplifying. A novel technique based on 85Kr for quantification of gas -liquid mass transfer in bioreactors.
A promising technique for quantification of the mass transfer coefficient k l a for oxygen in bioreactors is described. The method is based on injection of the volatile, inert 85 Kr isotope into the medium followed by measurement of the radioactivity in the gas leaving the head space.
The measured response is interpreted using a simple model for the gas flow through the bioreactor. The method is compared with two other methods: 1 a dynamic method based on N 2 and 2 the classical sulphite method. The isotope method compares well with the dynamic method and, from the comparison with the sulphite method, it is concluded that the sulphite method gives an overestimation of k l a which cannot be explained solely by reduced coalescence due to the electrolyte.
The extra effect is probably due to chemical reaction in the liquid film. The isotope method has been used to study the influence of the medium composition on the oxygen mass transfer. A major advantage of the 85 Kr method is that it can by applied during real process conditions as illustrated in an experiment with growth of Aspergillus oryzae. Views Total views. Actions Shares. No notes for slide. Chensolutions 1. An overhaul would have been reasonable after Run V logarithmic axis vs.
When V is constant runs 5 to 7 , plot lnZ vs. The results in part b are more reliable, because more data were used to obtain them. For the calculation of Part b to be correct, the density would have to be changed to its equivalent at 47oC. Presuming that the dependence of solution density on T is the same as that of pure water, the solution density at 47oC would be higher than 0. The ILE mass flow rate calculated in Part b is therefore too low.
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